To represent the decay of a radioactive substance that loses 5% of its total weight per day, you can use the exponential decay formula:
\[ f(x) = f_0 \cdot (1 - r)^x \]
where:
- \( f_0 \) is the initial weight (80 grams in this case),
- \( r \) is the decay rate (5% or 0.05),
- \( x \) is the number of days.
Since it loses 5%, the fraction remaining after one day is \( 1 - 0.05 = 0.95 \).
Therefore, the equation becomes:
\[ f(x) = 80 \cdot (0.95)^x \]
However, in the provided options, the equations all have a "-1" at the end, which is not appropriate for the decay function in this context.
Thus, if we only focus on finding the decay equation itself without the "-1", the correct choice would be:
f(x) = 80(0.95)^x
Since the provided options include an irrelevant "-1", none of the given options accurately represent the decay equation. If we consider just the functioning part without the "-1", we can conclude that:
The correct decay function is:
f(x) = 80(0.95)^x (not in your options).